The 35-year-old, who recently joined Millwall on loan until the end of the season, will be out of contract at Portman Road during the summer.
"Nothing's been decided totally, but there is every chance that [Edwards will be leaving] because he's out of contract," McCarthy is quoted as saying by the East Anglian Daily Times.
"At 35 he's not going to be getting any better, not that he's tailing off and getting any worse I might add because he's a very fit lad. At some stage though you start having to look to the future."
Edwards signed for the Tractor Boys from Sunderland back in 2009.